Odemwingie joined Cardiff from West Bromwich Albion in September of last year and scored twice in 17 league and cup appearances.
"We're delighted to have signed Peter. Things haven't perhaps gone as well for him at Cardiff as he would have hoped and he's really keen to start afresh with us," Stoke manager Mark Hughes told the club's website (www.stokecityfc.com).
Trinidad and Tobago forward Jones joined Stoke in 2010 and scored 13 times in 88 appearances.
His first-team opportunities have been limited this season and he was fined by the club after refusing to make himself available for the game against Liverpool earlier this month.
(Writing by Justin Palmer; editing by Martyn Herman)
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